A heat pump heating system aggregate day-ahead scheduling method and system considering multi-thermal inertia dynamic response and heat state recovery
Patent Information
- Application Number
- CN202611365359.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-09-04
- Publication Date
- 2026-10-23
AI Technical Summary
若恢复热量不与额外电输入功率建立闭环，优化模型可能出现恢复热量凭空产生的非物理解；若多个站点同时恢复，则还可能形成新的聚合电功率反弹峰值
[0060]有益效果：通过以持续时间内可用热流积分形成动态可达热量边界，使功率边界和能量边界与实际热过程和调节持续时间相匹配；通过区分电侧与热侧并按站点时变性能系数逐时换算，提高电网调用量的可追溯性；通过将热状态亏缺定义为相对基准真实热状态的能量偏差并经物理热流分配、真实状态边界和跨时段转移共同约束，减少亏缺变量与储热、管网或建筑真实状态脱离的风险；通过将恢复制热量与额外电输入功率经性能系数闭合，并设置恢复终点、反弹峰值和爬坡约束，实现削峰后恢复过程的显式规划；通过多站点错峰恢复和设备级指令分解与可行性校核，形成从动态边界计算到压缩机、水泵和阀门执行的完整闭环，便于对调节持续时间、执行功率、恢复窗口和反弹上限进行验证。
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Figure CN122960951A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to, in particular, a method and system for the aggregated day-ahead scheduling of a heat pump heating system that considers dynamic response of multiple thermal inertia and thermal state recovery. Background Technology
[0002] With the electrification of building heating and the large-scale application of heat pumps, heat pump loads are gradually becoming an important flexible resource for grid demand response, peak shaving, and renewable energy consumption. A heat pump heating system typically includes not only the heat pump unit but also a circulating water system, heating network, building thermal environment, and may be equipped with a hot water storage tank or other thermal storage devices depending on site conditions. These components have different heat capacities, heat transfer paths, and dynamic time scales.
[0003] Existing methods often provide fixed power boundaries or equivalent energy storage boundaries based on the heat pump's rated power, thermal storage capacity, indoor allowable temperature range, or heat load forecast results, and then perform day-ahead optimization. This representation can reduce model complexity, but if thermal storage, piping networks, and buildings are unified into a single equivalent energy storage unit, it is easy to overlook the impact of heat transport delay, thermal state change rate, and regulation duration on available capacity.
[0004] It is particularly important to distinguish between the electric side and the thermal side. Grid dispatch and aggregation assessments occur on the electric side, focusing on electrical power and energy; thermal storage, pipeline networks, and building condition margins occur on the thermal side, focusing on heating power, heat output, and temperature status. If thermal side margins are directly used as electric side flexibility, or if heat output is directly combined between multiple sites without their respective performance coefficients, the power boundary and energy boundary will lack traceable physical meaning.
[0005] When a heat pump participates in peak shaving by reducing its electrical input power, its heating capacity decreases simultaneously. The heat gap is temporarily filled by thermal storage, water in the pipe network, or building heat capacity, causing the actual thermal state to deviate from the normal baseline trajectory. The end of the adjustment does not mean this deviation disappears automatically; the system needs to recover through additional heating or other constrained heat sources in subsequent periods. If the recovered heat does not establish a closed loop with the additional electrical input power, the optimization model may exhibit non-physical solutions where the recovered heat is generated out of thin air; if multiple sites recover simultaneously, a new aggregated electrical power rebound peak may also form.
[0006] Furthermore, a slow change in a building's thermal state does not equate to a building's inability to participate in short-term electrical power regulation. The electrical power of a heat pump can decrease rapidly within the equipment's allowable limits, while observable changes in building room temperature may only appear after a period of time. Therefore, the electrical power response delay, heat transport delay, and thermal state observability delay should be described separately, and dynamic reachability should be constructed based on the actual available heat flow and the true thermal state boundary over the duration.
[0007] Therefore, there is a need for a day-ahead scheduling technology for heat pump heating systems that can simultaneously close time-dependent dynamic reachable boundaries, perform electrothermal conversion, transfer of real thermal deficit across time periods, couple recovery of heat and recovery of electrical power, multi-site peak-shifting recovery, and equipment-level execution verification. Summary of the Invention
[0008] Purpose of the invention: The purpose of this invention is to provide a method and system for aggregated day-ahead scheduling of heat pump heating systems that can overcome the difficulties of fixed flexible boundaries in reflecting the dynamic reachability of multiple thermal inertia under different durations, the mixing of thermal margin and electrical dispatch amount, the disconnect between thermal state deficit after load reduction and the actual state, the lack of electrical power source constraints for restoring heating capacity, and the insufficient feasibility of multi-site recovery rebound and equipment execution.
[0009] Technical solution: The day-ahead scheduling method for heat pump heating systems considering dynamic response of multiple thermal inertia and thermal state recovery as described in this invention includes:
[0010] Acquire the heat pump electrical input power, circulating water pump and auxiliary machine electrical power of each site, as well as the heating network, building thermal status and thermal storage status when thermal storage devices are configured, distinguish between electrical and thermal quantities and establish an electrical-thermal conversion relationship.
[0011] For each site, a physical thermal state model is established for at least two thermal inertia links to determine the thermal state, allowable operating boundary and characteristic response time, as well as at least one of the electrical power response delay, heat transport delay and thermal state observable delay, and the thermal state margin is calculated.
[0012] Based on the duration of the adjustment task, the dynamically attainable heat is obtained by integrating the available heat flux of each thermal inertia element within the duration, and the dynamic power and energy boundary on the electric side are generated according to the time-varying performance coefficient of the site and the power limit on the equipment side.
[0013] Obtain day-ahead heat load forecasts and external environment forecasts to determine the control reference power trajectory and reference thermal state trajectory for each site without additional grid regulation.
[0014] When the heat pump's electrical input power is lower than the control reference electrical power, the power reduction is converted into a reduction in heating capacity based on the time-varying performance coefficient of the site, and then allocated to each thermal inertia link; a cross-time period thermal state deficit and state transition relationship is established relative to the reference thermal state, while maintaining the physical boundary of the real thermal state.
[0015] A day-ahead optimization scheduling model is established. In the model, the heat pump electric input power, the heating gap undertaken by each thermal inertia link and the recovery heating are jointly optimized. The total recovery heating is constrained by the heat generated by the additional heat pump electric power through the time-varying performance coefficient. The recovery heating undertaken by other heat sources is separately included in the corresponding heat flow channel and state constraints. The allowable remaining deficit at the recovery endpoint, the upper limit of the aggregated electric power rebound and the ramp-up constraint of adjacent time periods are set.
[0016] The aggregation layer allocates external reduction targets under the constraints of local heating safety, dynamic reachability boundary, operating status and recovery demand of each site, and staggers the recovery time windows of different sites;
[0017] The site objectives are decomposed into equipment-level control commands, which are issued after feasibility verification. The dynamic boundaries, thermal deficiencies, and recovery plans that have not yet been executed are updated on a rolling basis based on the execution power with timestamps, equipment status, and thermal status feedback.
[0018] By distinguishing between electrical and thermal quantities and establishing an electrical-thermal conversion relationship, at least two thermal inertia links for each site are modeled and their characteristic response time and response delay are determined. Furthermore, the dynamic reachable heat is obtained by integrating the available heat flux based on the duration of the adjustment task, and the dynamic power and energy boundary of the electrical side are generated. This ensures that the site's adjustability matches the adjustment duration, the actual thermal state, and the dynamic response characteristics, avoiding boundary distortion caused by merging multiple types of heat capacity into a single equivalent energy storage, and also avoiding the inaccuracy of the fixed power boundary under both short-term and long-term adjustment.
[0019] By converting the reduction in electrical power into a reduction in heating capacity and establishing a cross-period relationship between the thermal state deficit and state transition relative to the baseline thermal state, the restored heating capacity is correlated with the additional heat pump electrical power via a time-varying performance coefficient. Furthermore, a recovery endpoint, an upper limit for polymerization rebound, and ramp-up constraints are set to ensure that the thermal state shift caused by the reduction has a traceable recovery requirement. The restored heat has a closed loop of electrical power sources, preventing the restored heat from being generated out of thin air and suppressing the polymerization rebound peak formed by simultaneous recovery at multiple sites.
[0020] By allocating external downsizing targets under site safety constraints through the aggregation layer and staggering recovery time windows, site targets are decomposed into equipment-level control commands and issued after feasibility verification. Dynamic boundaries and recovery plans are updated on a rolling basis based on timestamped feedback, so that scheduling results can be directly mapped to compressor, water pump and valve actions. Actual execution results can be fed back to correct subsequent scheduling, avoiding individual sites from exceeding their true thermal state boundaries.
[0021] Preferably, the thermal inertia element is selected from the thermal storage device, circulating water and heating network, building air and building envelope; for sites without independent thermal storage devices, at least the thermal inertia of the heating network and the building thermal inertia are used.
[0022] By limiting the selection of thermal inertia elements from thermal storage devices, circulating water and heating pipe networks, building air and building envelope, and stipulating that sites without independent thermal storage devices should at least use the thermal inertia of the heating pipe network and the building thermal inertia, it can be ensured that at least two types of thermal inertia elements are established under different site configuration conditions, avoiding the loss of dynamic response differences by merging multiple types of heat capacity into a single equivalent state.
[0023] Preferably, the power response delay is used to characterize the delay from the power control command to the station power reaching the set change threshold, the heat transfer delay is used to characterize the delay from the heat flow change on the heating side to the target thermal inertia link, and the thermal state observability delay is used to characterize the delay from the change in temperature or equivalent thermal state after the heat pump operation changes to produce an identifiable change; when the rate of change of the building thermal state is lower than the set value, the heat pump power can still be reduced for a short time within the allowable range of equipment operation constraints, and the duration is limited by the boundary of the building's actual thermal state.
[0024] By defining the power response delay, heat transport delay, and thermal state observability delay separately and clarifying their respective characterization objects, the difference between fast power response and slow thermal state evolution can be distinguished. By limiting the heat pump power to a short-term reduction within the equipment operation constraints when the rate of change of the building thermal state is lower than the set value, the short-term adjustment capability can be avoided due to the slow response of the building thermal state, and the building thermal inertia can be fully utilized while ensuring equipment safety.
[0025] As a preferred embodiment, the characteristic response time, as well as the power response delay, heat transfer delay, and thermal state observability delay, are identified for their respective input-output channels using a first-order inertial plus pure delay model for step operation data or natural disturbance data. The characteristic response time is the time corresponding to the preset proportion of the steady-state change after deducting the pure delay of the corresponding channel, and the various response delays are the time when the corresponding response quantity first continuously exceeds the measurement noise threshold. The parameters are re-identified using historical operation data after removing abnormal data according to a preset update cycle.
[0026] By using a first-order inertial plus pure delay model to identify characteristic response times and various response delays for each input-output channel, it is possible to obtain physically meaningful dynamic response parameters based on actual operating data, and to update them in a rolling manner as the operating state changes, thereby improving the accuracy of dynamic reachable heat calculation.
[0027] Preferably, the dynamically accessible heat is divided into upward and downward adjustments based on the scheduling scenario, wherein the downward adjustment of the dynamically accessible heat is calculated using the following formula:
[0028] ,
[0029] in, For the first The site's Thermal inertia element during duration The downward dynamic within can reach heat. For the first The site's The thermal inertia component reduces the thermal state margin at time interval t. For the first The site's Thermal inertia element at time The maximum available down-adjustable heat flux;
[0030] The effective flexibility contribution coefficient can be calculated based on the reduced dynamically attainable heat:
[0031] ,
[0032] in, For the first The site's Thermal inertia element during duration Effective flexibility contribution coefficient within; when hour, .
[0033] By providing a specific formula for calculating the dynamically available heat, the boundary calculations can be made deterministic and verifiable, avoiding the need to set the available energy ratio based solely on experience. By defining the effective flexibility contribution coefficient as the ratio of the dynamically available heat to the thermal state margin, and setting it to zero when the thermal state margin is zero, the available capacity of different thermal inertia links at different durations can be intuitively compared, providing a basis for allocating adjustment targets for the polymer layer.
[0034] Preferably, each station first calculates the dynamically available heat capacity and the actual heat capacity gap on the heat side, and then uses the performance coefficient of that station for that period to convert it into adjustable electrical energy on the electrical side; when spanning multiple scheduling periods, the total adjustable electrical energy over the adjustment duration is obtained by summing the performance coefficients of each period hourly. The specific calculation formula is as follows:
[0035] ,
[0036] in, For the first The site during the duration Internal adjustable electrical energy, For the first The site's Thermal inertia during time period Available heat For the first The performance coefficient of the site during time period r; the performance coefficient is determined based on the source-side temperature, water supply temperature and load rate, using manufacturer performance charts, online identification models or a combination of both.
[0037] By requiring each site to first calculate the dynamically available heat on the thermal side, and then convert it into electrical energy on the electrical side hourly according to the time-varying performance coefficient for each time period, and summing the results after conversion across multiple scheduling periods, the error caused by using a single performance coefficient to uniformly convert the total heat can be avoided, thus maintaining a traceable correspondence between the electrical side boundary and the thermal side state.
[0038] Preferably, the thermal state deficit is associated with the actual thermal state through a thermal state-heat mapping function; when the thermal state is a single temperature state, the thermal state-heat mapping uses linear conversion based on equivalent heat capacity.
[0039] and ,
[0040] in, For the first The first adjustment task The first site The thermal inertia element during the time period Thermal deficit For the first The site's The equivalent heat capacity of the thermal inertia element. and The first The first site The thermal inertia element during the time period The reference thermal state and the actual thermal state; and The first The first site The minimum and maximum thermal states of a thermal inertia element;
[0041] When the thermal state is a vector, the corresponding energy function is used for mapping:
[0042] ,
[0043] in, For the first The first site The thermal state-heat mapping function of a thermal inertia element.
[0044] By defining the thermal state deficit and relating it to the actual thermal state through a thermal state-heat mapping function, and providing mapping methods for single-temperature states and multi-dimensional states respectively, while maintaining the physical boundaries of the actual thermal state, it can prevent the deficit variable from deviating from the thermal storage temperature, supply and return water temperature or room temperature, and ensure that the recovery plan is based on the actual physical state.
[0045] As a preferred option, when the recovery windows of different adjustment tasks overlap, the deficit state of each task is saved separately, and the recovery heating capacity, equipment power and actual thermal state constraints of the same site at the same time period are jointly verified.
[0046] As a preferred option, the necessary decision variables for the current optimized scheduling model include at least the heat pump electrical input power, thermal deficit, and recovery heating capacity; the optimization objective includes at least the external downsizing command tracking deviation and the recovery rebound term, expressed as:
[0047] ,
[0048] in, The target was lowered due to external factors. To aggregate the actual response volume, To achieve the maximum rebound power during the recovery phase, This represents the change in polymer electric power. and These represent the weights of the rebound and ramp-up terms, respectively; optimization objectives may also include one or more of the following: operating costs, number of start-ups and shutdowns, water supply temperature deviation, and building thermal comfort deviation.
[0049] By limiting the necessary decision variables of the day-ahead optimization scheduling model to at least include heat pump electrical input power, thermal deficit, and recovery heating capacity, and by providing a specific expression for the optimization objective, the model can suppress recovery rebound and power ramp-up while ensuring tracking of external down-regulation commands. At the same time, it can expand the economic and comfort objectives according to actual needs, giving the optimization model a clear solution structure and configurability.
[0050] The day-ahead scheduling system for heat pump heating systems that considers dynamic response and thermal state recovery based on multiple thermal inertia, as described in this invention, includes:
[0051] The site data acquisition module is used to acquire the heat pump electrical input power, circulating water pump and auxiliary machine electrical power of each site, as well as the heating network, building thermal status and thermal storage status when the thermal storage device is configured, to distinguish between electrical and thermal quantities and to establish an electrical-thermal conversion relationship.
[0052] The multi-thermal inertia state and parameter identification module is used to establish a physical thermal state model for at least two thermal inertia links at each site, determine the thermal state, allowable operating boundary and characteristic response time, as well as at least one of electrical power response delay, heat transport delay and thermal state observable delay, and calculate the thermal state margin.
[0053] The duration dynamic reachable boundary generation module is used to obtain the dynamically reachable heat based on the available heat flux integral of each thermal inertia element within the duration, according to the adjusted task duration.
[0054] The electricity-heat conversion module is used to convert the dynamic available heat, heating capacity gap and recovery heat capacity on the heat side into electricity power or electrical energy based on the heat pump performance coefficient of each site and time period.
[0055] The control reference trajectory module is used to obtain day-ahead heat load forecasts and external environment forecasts, and to determine the control reference power trajectory and reference thermal state trajectory of each site without the participation of additional grid regulation.
[0056] The thermal state deficit and recovery module is used to convert the power reduction amount into the heating capacity reduction amount according to the time-varying performance coefficient of the site when the heat pump electrical input power is lower than the control reference electrical power, and distribute it to each thermal inertia link; establish the cross-time thermal state deficit and state transition relationship relative to the reference thermal state, while maintaining the physical boundary of the real thermal state.
[0057] The aggregation target allocation and peak recovery module is used to establish a day-ahead optimization scheduling model. In the model, the heat pump electric input power, the heating gap undertaken by each thermal inertia link and the recovered heating are jointly optimized so that the total recovered heating is constrained by the heat generated by the additional heat pump electric power through the time-varying performance coefficient. The recovered heating undertaken by other heat sources is separately included in the corresponding heat flow channel and state constraints, and the allowed remaining deficit at the recovery endpoint, the upper limit of the aggregation electric power rebound and the ramp-up constraint of adjacent time periods are set.
[0058] The device-level instruction decomposition and feasibility verification module is used by the aggregation layer to allocate external reduction targets under the constraints of local heating safety, dynamic reachability boundary, operating status and recovery demand of each site, and to stagger the recovery time windows of different sites; it decomposes the site targets into device-level control instructions, which are then issued after feasibility verification.
[0059] The feedback rolling update module is used to provide rolling updates of unexecuted dynamic boundaries, thermal deficits, and recovery plans based on timestamped execution power, device status, and thermal status feedback.
[0060] Beneficial effects: By forming a dynamically reachable heat boundary using the integral of available heat flux over a duration, the power and energy boundaries are matched with the actual thermal process and regulation duration; by distinguishing between the electrical and thermal sides and converting them hourly according to the time-varying performance coefficients of each site, the traceability of grid dispatch is improved; by defining thermal state deficit as an energy deviation relative to the reference true thermal state and constraining it through physical heat flux allocation, true state boundary, and cross-time period transfer, the risk of deficit variables deviating from the true state of thermal storage, pipelines, or buildings is reduced; by closing the recovery heating capacity and additional electrical input power through performance coefficients and setting recovery endpoints, rebound peaks, and ramp-up constraints, explicit planning of the recovery process after peak shaving is achieved; through multi-site peak shaving recovery and equipment-level command decomposition and feasibility verification, a complete closed loop is formed from dynamic boundary calculation to compressor, pump, and valve execution, facilitating the verification of regulation duration, execution power, recovery window, and rebound upper limit. Attached Figure Description
[0061] Figure 1 This is the overall flowchart of the method of the present invention;
[0062] Figure 2 This is a schematic diagram of the dynamic response and flexible dispatching mechanism for multiple thermal inertia of the present invention;
[0063] Figure 3 This is a schematic diagram showing the relationship between the effective flexibility contribution coefficient of different thermal inertia links of the present invention and the adjustment duration. Detailed Implementation
[0064] As shown in the figure, the aggregation-day-ahead scheduling method for heat pump heating systems considering dynamic response and thermal state recovery, as described in this invention, is applied to aggregation control systems containing at least one heat pump heating station. The aggregator first establishes a station list and creates electrical and thermal measurement fields for each station. The heat pump electrical input power, circulating water pump, and necessary auxiliary equipment electrical power are measured on the electrical side, while the heat pump heating power, thermal storage / pipeline / building thermal state, dynamically available heat, thermal state deficit, and recoverable heat are measured on the thermal side. The coefficient of performance (COP) is updated independently by station and time period.
[0065] S1. Obtain system operating data and establish the current operating status, and at the same time establish the conversion relationship between electrical and thermal quantities.
[0066] For each heat pump heating station in the aggregate object This involves obtaining the heat pump's electrical input power, the circulating water pump's power, and the power of necessary auxiliary equipment; obtaining the heat pump's supply and return water temperatures, flow rates, heating network node or equivalent temperatures, indoor temperatures, and the building's equivalent thermal state; and, when configuring a thermal storage device, further obtaining the thermal storage temperature, charging and discharging status, and thermal storage-side flow rate. All electrical power is based on... This indicates that the electrical energy is... Indicates; all heating power is in the range of This indicates that heat, thermal state margin, deficit, and recovery are... express.
[0067] Coefficient of performance of heat pump Instead of using a single fixed value across the entire time domain, the value is determined based on the source-side temperature, supply water temperature, and partial load rate, using the manufacturer's performance charts, operational data identification models, or a combination of both, and updated according to the scheduling period. The heat pump heating power and heat pump electrical input power satisfy the following:
[0068] ,
[0069] in, Indicates the first Each site during the time period The heating power of the heat pump Indicates the first Each site during the time period The coefficient of performance of heat pumps, Indicates the first Each site during the time period The heat pump's electrical input power; the superscripts th and el represent the thermal side and electrical side, respectively.
[0070] The total electrical power used by a site or aggregate object when participating in grid response also includes the electrical power of circulating water pumps and necessary auxiliary equipment:
[0071] ,
[0072] in, For aggregated objects in time periods Total aggregate electrical power, and The first Each site's heat pumps, circulating water pumps, and necessary auxiliary electrical power.
[0073] S2. Divide the thermal inertia components and identify the thermal state, characteristic response time, and response delay.
[0074] Based on the site's physical structure, the states capable of handling heat gaps are divided into at least two types of thermal inertia elements, which are selected from thermal storage devices, circulating water and heating pipe networks, and building air and building envelope. For sites without independent thermal storage devices, it is not mandatory to set thermal storage state variables.
[0075] Establish a state equation for each thermal inertia element. ,in For the true thermal state, This refers to the heat flow or control quantity acting on this process. This is due to disturbances such as outdoor weather, building heat load, or user heating demand. The actual thermal state satisfies the requirements throughout the entire optimization time domain. ;in, and They represent the first The first site The minimum and maximum allowable thermal states of a thermal inertia element. Indicates time period The true thermal state.
[0076] Three types of delay are defined: electrical power response delay Characterizing the time from equipment control command to power reaching a set change threshold; heat transfer delay. Characterizing the time it takes for a change in heat flow to propagate to the target thermal inertia element; thermal state observability delay Characterizes the time it takes for a identifiable change to occur in temperature or equivalent thermal state. The three types of delays are not interchangeable. A larger value only indicates that the thermal state changes slowly, not that the heat pump power cannot be reduced immediately. When the building's thermal state changes slowly, the heat pump power can still be reduced for a short time within the limits allowed by the equipment's operating constraints, and the duration is limited by the building's actual thermal state boundary.
[0077] Parameter identification for step-based operational data or natural disturbance data can be performed using a first-order inertial plus pure delay model:
[0078] ,
[0079] in, Indicates the first Response volume at each stage Indicates the initial response quantity. Represents steady-state gain. Indicates the pure delay time. Indicates the characteristic response time. This represents the unit step function.
[0080] In this embodiment The time it takes for the response to reach 63.2% of its steady-state change after deducting the pure delay; The time it takes for the response quantity to first continuously exceed the measured noise threshold is defined. The noise threshold can be three times the steady-state noise standard deviation or a preset engineering threshold. For heating networks, It can also be estimated from the effective pipe length and average flow velocity. Parameter identification uses continuous historical data with a preset sampling period, first removing sensor over-range, communication interruption and obvious anomalies, and then updating it on a rolling basis according to the preset period.
[0081] Calculate the thermal state margin based on the actual thermal state and allowable boundaries. The thermal inertia of the thermal storage device, heating network, and building can be calculated using the following formula to determine the downward adjustment margin:
[0082] ,
[0083] ,
[0084] ,
[0085] in, This indicates the downward adjustment thermal state margin of the thermal storage device. For the quality of the heat storage medium, The specific heat capacity of water, The current thermal storage temperature, This is the lower limit of the permissible temperature for the thermal storage device; This indicates the margin for adjusting the heating status of the heating network. This indicates the density of water. Indicates the effective water volume of the pipe network. This indicates the specific heat capacity of water. and These represent the current and minimum allowable pipe network temperatures, respectively. This indicates the downward adjustment thermal state margin of the building's thermal inertia. Indicates the building's equivalent heat capacity. Indicates the current indoor temperature. This indicates the minimum permissible indoor temperature.
[0086] The adjustment margin of the thermal storage device is calculated according to the following formula.
[0087] ,
[0088] in, To allow for an upward adjustment margin for the thermal storage device, This represents the upper limit of the allowable temperature for the thermal storage device.
[0089] The mass of the thermal storage medium, the effective water volume of the pipeline network, and the equivalent heat capacity of the building are obtained through design parameters, field tests, or model identification. When the thermal state is a multi-dimensional vector, the corresponding energy function is used. The heat capacity is not calculated by directly multiplying the state vector by a single scalar heat capacity.
[0090] S3. Calculate the dynamic reachable heat and effective flexibility contribution related to duration, and generate dynamic flexibility boundaries.
[0091] In this article, "dynamically available heat" is a general term for situations where the adjustment direction is not specified; the scenario of downward adjustment is referred to as downward adjustment of dynamically available heat, and the scenario of upward adjustment is referred to as upward adjustment of dynamically available heat.
[0092] In the Duration of each adjustment task Within this framework, the dynamically attainable heat is obtained by integrating the heat flux of each thermal inertia element over its duration. Then, based on the time-varying performance coefficients of the site and the power constraints on the equipment side, the dynamic power and electrical energy boundary on the electrical side are generated. The formula for reducing the dynamically attainable heat is as follows:
[0093] ,
[0094] in, Indicates the first The first site The thermal inertia element during the duration The downward dynamic within can reach heat. This indicates that the thermal margin has been reduced in this stage. Indicates time The maximum available down-regulation heat flux is determined by the thermodynamic process, hydraulic state, valve state, terminal load, and actual thermal state.
[0095] The effective flexibility contribution coefficient is the ratio of the dynamically available heat to the thermal state margin for the corresponding scenario. In the downgraded scenario, it is the ratio of the downgraded dynamically available heat to the downgraded thermal state margin.
[0096] ,and ,
[0097] in, This represents the effective flexibility contribution coefficient, with a value ranging from 0 to 1. Indicates the dynamically attainable heat. This indicates a current downward adjustment of the thermal state margin. When... When, define .
[0098] In the first-order inertial heat flow approximation used for illustrative purposes only, if a heat transport delay does indeed exist in a certain stage... The available heat flux can be written in the following segmented form; Not equivalent to the observable delay of building thermal state .
[0099] ,
[0100] ,
[0101] in, Indicates the first The thermal inertia element at time... The maximum available down-adjustable heat flux, This indicates a delay in heat delivery. This indicates the upper limit of the available heat flux in steady state. Indicates the characteristic response time.
[0102] Therefore, the effective flexibility contribution coefficient It represents the proportion of dynamically available heat over a given period to the current thermal state margin. Figure 3 This illustrates the overall pattern of how the effective flexibility contribution of different thermal inertia stages changes with the duration of adjustment. The specific values are determined by the dynamically available heat, the true thermal state boundary, and the available heat flux. For building thermal inertia, a short-term downsizing can be buffered by the thermal comfort margin, with its electrical power responding first, followed by the duration being limited by the building state equation.
[0103] Each site first obtains the dynamic availability of heat on the thermal side, and then converts it to the electrical side hourly according to the local time-varying COP. When spanning multiple scheduling periods, a single COP is not used to uniformly convert the total heat; instead, it is calculated according to the COP of each time period. Sum after conversion:
[0104] ,
[0105] in, Indicates the first Each site during the duration The internal adjustable power supply Indicates the first The first site The thermal inertia element during the time period Available heat Indicates the first The performance coefficient of each site during time period r.
[0106] ,
[0107] in, Indicates the first Each site during the duration The adjustable power boundary below, Indicates the first The power limit can be lowered on the equipment side of each site. This indicates that the corresponding power can be reduced. The dynamic boundary of the site's power side is composed of the site's power boundary and power boundary. When aggregating multiple sites, only the feasible set of electrical side devices that have already undergone site-level electrothermal conversion is aggregated.
[0108] In the text, i represents the station number, j represents the heat cycle number, k represents the task number, and t and r represent the time period number, which will not be elaborated further below.
[0109] S4. Obtain heat load forecasts and environmental forecasts, and determine the control baseline operating trajectory.
[0110] Obtain the day-ahead dispatch cycle's heat load forecast, outdoor temperature, solar radiation, wind speed, and optional electricity prices, renewable energy output, or grid regulation demand. Calculate the control baseline trajectory based on the forecast data, assuming the site does not participate in additional power regulation. This benchmark is used for optimizing scheduling, calculating heating deficit, and defining thermal state deficit. Among these, This represents the control baseline trajectory of the i-th station during time period t; This represents the control reference power of the i-th station when it does not participate in additional power regulation during time period t; This represents the baseline thermal state of the i-th site during time period t when it does not participate in additional power regulation.
[0111] When project acceptance or third-party measurement verification requires independent determination of the actual peak-shaving amount, a separate measurement verification baseline shall be defined. The measurement verification baseline can be generated according to the corresponding test rules based on typical days, meteorological corrections, and measured loads. Its purpose is only to calculate the actual response, peak shaving depth, and assessment indicators, and it does not replace the control baseline trajectory.
[0112] S5. Calculate the reduction in heating capacity and establish the thermal state deficit and its state transition relationship across time periods.
[0113] From the perspective of the power grid, the reduction is defined as a decrease in electrical power. When the electrical input power of a heat pump at a certain site is lower than the control baseline, the reduction in heating capacity is defined using a non-negative definition:
[0114] ,
[0115] in, This indicates the reduction in heating capacity caused by demand response. Indicates the control reference power. Indicates the scheduling time interval; This ensures that the reduction in heating capacity is non-negative. In this formula... use , use The calculation result is . Multiply by the change in electrical power to obtain the change in heating capacity on the hot side.
[0116] The reduction in calorific value cannot be arbitrarily allocated through completely free proportional variables, but should be determined by the actual calorific value borne by each stage of the process. It is determined that the conservation of heat and the dynamic achievable upper limit are satisfied:
[0117] ,
[0118] in, Indicates the first In the first adjustment task The thermal inertia element during the time period The actual heating capacity shortfall, This indicates the reduction in the total heating capacity of the station. This indicates the maximum achievable dynamic limit for this stage. Actual heat output. It can be calculated from heat flux sensors, hydraulic topology, flow rate, and temperature difference; when direct sensors are lacking, it can be estimated from heat flux participation factors or state sensitivity identified through historical data. If the optimization model directly determines the participation ratio, then it is necessary to simultaneously establish a mapping between this ratio and valve, flow rate, or station-end control variables.
[0119] For the One regulation task defines thermal state deficit as the energy deviation relative to the control reference thermal state:
[0120] ,
[0121] in, Indicates the first The first adjustment task The first site The thermal inertia element during the time period Thermal deficit The mapping function representing the thermal state to heat. and These represent the reference thermal state and the actual thermal state, respectively.
[0122] For a single temperature state, it can degenerate into a linear form of equivalent heat capacity:
[0123] ,
[0124] in, Indicates the first The first site The equivalent heat capacity of a thermal inertia element. and These represent the reference thermal state and the actual thermal state, respectively.
[0125] The deficit status in the current forecast phase is transmitted across time periods using the following formula:
[0126] ,
[0127] in, The coefficient representing the preservation or natural evolution of thermal state deficiency. This indicates a new heating capacity shortfall. This indicates that the heating capacity has been restored; This represents the thermal state deficit for the next time period. During system rolling operation, the latest measured or estimated true thermal state is used. Recalculate This is to avoid the deficit variables deviating from the actual thermal storage temperature, supply and return water temperature, or room temperature.
[0128] S6. Establish a regulation-recovery coordinated constraint and day-ahead optimization scheduling model.
[0129] Each adjustment task Each recovery phase has an independent start time, recovery time window, and recovery end point. Heat generated during the recovery phase must not be created out of thin air. If the recovery is assumed to be handled by a heat pump, the total recovery heat output is constrained by the heat generated by the heat pump's additional electrical input power relative to the control reference through a time-varying COP. If a thermal storage device, waste heat, or other heat source participates in the recovery, its recovery heat flux is listed separately and satisfies its own energy state and power limit constraints.
[0130] ,
[0131] in, This indicates the recovery heat capacity of each thermal inertia component and its adjustment task. This indicates the recovered heat provided by heat storage, waste heat, or other heat sources; the first item on the right indicates the recovered heat obtained by converting the additional electrical input of the heat pump into COP.
[0132] Each thermal inertia element satisfies the following at the end of its corresponding recovery window:
[0133] ,
[0134] in, Indicates the first The recovery endpoint time corresponding to each adjustment task. This indicates the maximum thermal state deficit that the thermal inertia element is allowed to retain at the end of the recovery process.
[0135] To suppress polymerization rebound after the adjustment period ends, both a maximum polymerization power limit and a ramp-up constraint for adjacent time periods are set:
[0136] ,
[0137] ,
[0138] in, Indicates the aggregate control reference power. This indicates the allowable rebound margin. This represents the maximum ramp-up of aggregated electrical power in adjacent time periods.
[0139] When multiple adjustment events exist within the same day's scheduling period, for , Both the endpoint and the recovery endpoint retain the task index. When recovery windows overlap, the deficit for each task is recorded separately, but the equipment power, total restored heating capacity, and actual thermal status of the same site are checked uniformly.
[0140] S7. Solve the day-ahead optimization scheduling model, complete the multi-site adjustment target allocation, and generate load adjustment and thermal state recovery instructions.
[0141] The necessary decision variables for the current optimization model include at least the heat pump electrical input power, thermal deficit, and recovery heating capacity; its core objective is to track external down-regulation commands and reduce recovery rebound and power ramp-up, which can be written as:
[0142] ,
[0143] in, Indicates time period External downward adjustment targets, This represents the actual aggregate response. This indicates the maximum rebound power during the recovery phase. This represents the change in polymeric electrical power. and These represent the weights of the rebound and ramp-up terms, respectively. Without changing the core constraint chain, subordinate objectives such as operating costs, equipment start-up and shutdown frequency, water supply temperature deviation, and building comfort deviation can be further added.
[0144] The aggregator receives data from various sites. ,current Based on equipment status and recovery requirements, external adjustment targets are allocated within the local security constraints of each site. The actual response quantity of the aggregation layer is defined as:
[0145] ,
[0146] in, The downward adjustment target is given to the external power grid or the aggregation layer; For the first Each station controls the reference electrical power. The difference between the actual or planned power of the station is used to construct the external regulation command tracking deviation term.
[0147] Aggregate feasible sets Use symbols This represents the aggregation of feasible sets for each site under local dynamic boundaries, true thermal states, recovery endpoints, and device executable constraints, and is not an aggregation of the thermal side. or The results are directly added together. The recovery windows of multiple sites are staggered to ensure that the upper limit of the aggregation layer rebound and the ramp constraint are satisfied simultaneously.
[0148] S8. Decompose the scheduling instructions into device-level control instructions, complete the feasibility verification, and update them on a rolling basis based on feedback.
[0149] The target electrical input power of a station-level heat pump is not directly equivalent to the compressor frequency, pump frequency, or valve opening. A station-level instruction decomposer or secondary optimizer is installed to solve for the compressor frequency, pump frequency, valve opening, and heat storage charging / discharging state based on the compressor performance profile or identification model, circulating water pump power model, flow-head constraints, supply and return water temperature difference, valve characteristics, equipment start-up / shutdown and ramp-up constraints. Before issuing the instruction, the station's electrical power, heat flux, and state changes are recalculated; if the feasibility conditions are not met, the assignment is rolled back or redistributed.
[0150] The execution log records the adjustment task number, instruction timestamp, site target power, equipment control quantity, feedback power, key temperature, and execution status. The aggregator reads feedback and updates the log for periods not yet executed according to preset time intervals. , and recovery plan.
[0151] For prediction uncertainty, the thermal state margin can be contracted based on the standard deviation of the prediction error, quantiles, or confidence boundaries. For example:
[0152] ,
[0153] in, This represents the safety thermal state margin after correction for predicted uncertainties. Indicates the initial thermal margin. The coefficient corresponding to the target confidence level. This represents the standard deviation of the thermal state prediction error. This represents the equivalent heat capacity. The thermal state margin, power boundary, and electrical energy boundary are all constrained to be non-negative after contraction.
[0154] For scenarios involving increased valley filling or green electricity consumption, these should not be correlated with decreased deficits. They share the same state variables, while defining thermal state surplus. :
[0155] ,
[0156] in, This represents the thermal state surplus relative to the reference thermal state. The mapping function representing the thermal state to heat. and These represent the actual thermal state and the baseline thermal state, respectively. The upward adjustment scenarios each construct an upward adjustment thermal state margin. , Adjusting dynamics can achieve heat The upper boundary of the electrical side and the subsequent release and regression of the benchmark constraint are used to avoid overestimating the valley filling capacity due to the failure of the upper limit of the state to close.
[0157] The day-ahead scheduling system for heat pump heating systems that considers dynamic response and thermal state recovery based on multiple thermal inertia, as described in this invention, includes:
[0158] The site data acquisition module is used to acquire the heat pump electrical input power, circulating water pump and auxiliary machine electrical power of each site, as well as the heating network, building thermal status and thermal storage status when the thermal storage device is configured, to distinguish between electrical and thermal quantities and to establish an electrical-thermal conversion relationship.
[0159] The multi-thermal inertia state and parameter identification module is used to establish a physical thermal state model for at least two thermal inertia links at each site, determine the thermal state, allowable operating boundary and characteristic response time, as well as at least one of electrical power response delay, heat transport delay and thermal state observable delay, and calculate the thermal state margin.
[0160] The duration dynamic reachable boundary generation module is used to obtain the dynamically reachable heat based on the available heat flux integral of each thermal inertia element within the duration, according to the adjusted task duration.
[0161] The electricity-heat conversion module is used to convert the dynamic available heat, heating capacity gap and recovery heat capacity on the heat side into electricity power or electrical energy based on the heat pump performance coefficient of each site and time period.
[0162] The control reference trajectory module is used to obtain day-ahead heat load forecasts and external environment forecasts, and to determine the control reference power trajectory and reference thermal state trajectory of each site without the participation of additional grid regulation.
[0163] The thermal state deficit and recovery module is used to convert the power reduction amount into the heating capacity reduction amount according to the time-varying performance coefficient of the site when the heat pump electrical input power is lower than the control reference electrical power, and distribute it to each thermal inertia link; establish the cross-time thermal state deficit and state transition relationship relative to the reference thermal state, while maintaining the physical boundary of the real thermal state.
[0164] The aggregation target allocation and peak recovery module is used to establish a day-ahead optimization scheduling model. In the model, the heat pump electric input power, the heating gap undertaken by each thermal inertia link and the recovered heating are jointly optimized so that the total recovered heating is constrained by the heat generated by the additional heat pump electric power through the time-varying performance coefficient. The recovered heating undertaken by other heat sources is separately included in the corresponding heat flow channel and state constraints, and the allowed remaining deficit at the recovery endpoint, the upper limit of the aggregation electric power rebound and the ramp-up constraint of adjacent time periods are set.
[0165] The device-level instruction decomposition and feasibility verification module is used by the aggregation layer to allocate external reduction targets under the constraints of local heating safety, dynamic reachability boundary, operating status and recovery demand of each site, and to stagger the recovery time windows of different sites; it decomposes the site targets into device-level control instructions, which are then issued after feasibility verification.
[0166] The feedback rolling update module is used to provide rolling updates of unexecuted dynamic boundaries, thermal deficits, and recovery plans based on timestamped execution power, device status, and thermal status feedback.
Claims
1. A day-ahead scheduling method for a heat pump heating system considering dynamic response of multiple thermal inertia and thermal state recovery, characterized in that, include: Acquire the heat pump electrical input power, circulating water pump and auxiliary machine electrical power of each site, as well as the heating network, building thermal status and thermal storage status when thermal storage devices are configured, distinguish between electrical and thermal quantities and establish an electrical-thermal conversion relationship. For each site, a physical thermal state model is established for at least two thermal inertia links to determine the thermal state, allowable operating boundary and characteristic response time, as well as at least one of the electrical power response delay, heat transport delay and thermal state observable delay, and the thermal state margin is calculated. Based on the duration of the adjustment task, the dynamically attainable heat is obtained by integrating the available heat flux of each thermal inertia element within the duration, and the dynamic power and energy boundary on the electric side are generated according to the time-varying performance coefficient of the site and the power limit on the equipment side. Obtain day-ahead heat load forecasts and external environment forecasts to determine the control reference power trajectory and reference thermal state trajectory for each site without additional grid regulation. When the heat pump's electrical input power is lower than the control reference electrical power, the power reduction is converted into a reduction in heating capacity based on the time-varying performance coefficient of the site, and then allocated to each thermal inertia link; a cross-time period thermal state deficit and state transition relationship is established relative to the reference thermal state, while maintaining the physical boundary of the real thermal state. A day-ahead optimization scheduling model is established. In the model, the heat pump electric input power, the heating gap undertaken by each thermal inertia link and the recovery heating are jointly optimized. The total recovery heating is constrained by the heat generated by the additional heat pump electric power through the time-varying performance coefficient. The recovery heating undertaken by other heat sources is separately included in the corresponding heat flow channel and state constraints. The allowable remaining deficit at the recovery endpoint, the upper limit of the aggregated electric power rebound and the ramp-up constraint of adjacent time periods are set. The aggregation layer allocates external reduction targets under the constraints of local heating safety, dynamic reachability boundary, operating status and recovery demand at each site, and staggers the recovery time windows of different sites; The site objectives are decomposed into equipment-level control commands, which are issued after feasibility verification. The dynamic boundaries, thermal deficiencies, and recovery plans that have not yet been executed are updated on a rolling basis based on the execution power with timestamps, equipment status, and thermal status feedback.
2. The method according to claim 1, characterized in that, The thermal inertia components are selected from thermal storage devices, circulating water and heating pipe networks, building air and building envelope; sites without independent thermal storage devices shall at least use the thermal inertia of the heating pipe network and the building thermal inertia.
3. The method according to claim 1, characterized in that, The power response delay is used to characterize the delay from the time the power of the electrical control command to the station reaches the set change threshold. The heat transfer delay is used to characterize the delay from the time the heat flow change on the heating side to the time the target thermal inertia link is propagated. The thermal state observability delay is used to characterize the delay from the time the temperature or equivalent thermal state changes after the heat pump operation changes. When the rate of change of the building's thermal state is lower than the set value, the heat pump's electrical power can still be reduced for a short period within the allowable range of equipment operation constraints, and the duration is limited by the building's actual thermal state boundary.
4. The method according to claim 1, characterized in that, Characteristic response time, as well as power response delay, heat transfer delay, and thermal state observability delay, are identified for their respective input-output channels using a first-order inertial plus pure delay model for step operation data or natural disturbance data. Characteristic response time is the time corresponding to the preset proportion of steady-state change after deducting the pure delay of the corresponding channel. Various response delays are the time when the corresponding response quantity first continuously exceeds the measurement noise threshold. Parameters are re-identified using historical operation data after removing abnormal data according to a preset update cycle.
5. The method according to claim 1, characterized in that, The dynamically accessible heat capacity is divided into upward and downward adjustments based on the scheduling scenario. The downward adjustment of the dynamically accessible heat capacity is calculated using the following formula: ， in, For the first The site's Thermal inertia element during duration The downward dynamic within can reach heat. For the first The site's The thermal inertia component reduces the thermal state margin at time interval t. For the first The site's Thermal inertia element at time The maximum available down-adjustable heat flux; The effective flexibility contribution coefficient can be calculated based on the reduced dynamically attainable heat: ， in, For the first The site's Thermal inertia element during duration Effective flexibility contribution coefficient within; when hour, .
6. The method according to claim 1, characterized in that, Each station first calculates the dynamically available heat and the actual heat capacity gap on the heat side, and then uses the performance coefficient of the station for that period to convert it into adjustable electrical energy on the electrical side. When spanning multiple scheduling periods, the total adjustable energy over the regulation duration is obtained by summing the results after hourly conversion based on the performance coefficients of each period. The specific calculation formula is as follows: ， in, For the first The site during the duration Internal adjustable electrical energy, For the first The site's Thermal inertia in time period Available heat For the first The site's performance coefficient during time period r; The performance coefficient is determined based on the source-side temperature, supply water temperature, and load rate, using manufacturer performance charts, online identification models, or a combination of both.
7. The method according to claim 1, characterized in that, The thermal state deficit is associated with the actual thermal state through a thermal state-heat mapping function; when the thermal state is a single temperature state, the thermal state-heat mapping uses linear conversion based on equivalent heat capacity. and , in, For the first The first adjustment task The first site The thermal inertia element during the time period Thermal deficit For the first The site's The equivalent heat capacity of the thermal inertia element. and The first The first site The thermal inertia element during the time period The reference thermal state and the actual thermal state; and The first The first site The minimum and maximum thermal states of a thermal inertia element; When the thermal state is a vector, the corresponding energy function is used for mapping: ， in, For the first The first site The thermal state-heat mapping function of a thermal inertia element.
8. The method according to claim 1, characterized in that, When the recovery windows of different adjustment tasks overlap, the deficit status of each task is saved separately, and the recovery heating capacity, equipment power and actual thermal state constraints of the same site at the same time period are jointly checked.
9. The method according to claim 1, characterized in that, The necessary decision variables for optimizing the scheduling model currently include at least the heat pump electrical input power, thermal deficit, and recovery heating capacity; the optimization objective includes at least the tracking deviation of external downsizing commands and the recovery rebound term, expressed as: ， in, The target was lowered due to external factors. To aggregate the actual response volume, To achieve the maximum rebound power during the recovery phase, This represents the change in polymer electric power. and These represent the weights of the rebound term and the ramp term, respectively; the optimization objectives may also include one or more of the following: operating costs, number of start-ups and shutdowns, water supply temperature deviation, and building thermal comfort deviation.
10. A day-ahead scheduling system for a heat pump heating system considering dynamic response of multiple thermal inertia and thermal state recovery, characterized in that, include: The site data acquisition module is used to acquire the heat pump electrical input power, circulating water pump and auxiliary machine electrical power of each site, as well as the heating network, building thermal status and thermal storage status when the thermal storage device is configured, to distinguish between electrical and thermal quantities and to establish an electrical-thermal conversion relationship. The multi-thermal inertia state and parameter identification module is used to establish a physical thermal state model for at least two thermal inertia links at each site, determine the thermal state, allowable operating boundary and characteristic response time, as well as at least one of electrical power response delay, heat transport delay and thermal state observable delay, and calculate the thermal state margin. The duration dynamic reachable boundary generation module is used to obtain the dynamically reachable heat based on the available heat flux integral of each thermal inertia element within the duration, according to the adjusted task duration. The electricity-heat conversion module is used to convert the dynamic available heat, heating capacity gap and recovery heat capacity on the heat side into electricity power or electrical energy based on the heat pump performance coefficient of each site and time period. The control reference trajectory module is used to obtain day-ahead heat load forecasts and external environment forecasts, and to determine the control reference power trajectory and reference thermal state trajectory of each site without the participation of additional grid regulation. The thermal state deficit and recovery module is used to convert the power reduction amount into the heating capacity reduction amount according to the time-varying performance coefficient of the site when the heat pump electrical input power is lower than the control reference electrical power, and distribute it to each thermal inertia link; establish the cross-time thermal state deficit and state transition relationship relative to the reference thermal state, while maintaining the physical boundary of the real thermal state. The aggregation target allocation and peak recovery module is used to establish a day-ahead optimization scheduling model. In the model, the heat pump electric input power, the heating gap undertaken by each thermal inertia link and the recovered heating are jointly optimized so that the total recovered heating is constrained by the heat generated by the additional heat pump electric power through the time-varying performance coefficient. The recovered heating undertaken by other heat sources is separately included in the corresponding heat flow channel and state constraints, and the allowed remaining deficit at the recovery endpoint, the upper limit of the aggregation electric power rebound and the ramp-up constraint of adjacent time periods are set. The device-level instruction decomposition and feasibility verification module is used by the aggregation layer to allocate external reduction targets under the constraints of local heating safety, dynamic reachability boundary, operating status and recovery demand of each site, and to stagger the recovery time windows of different sites; it decomposes the site targets into device-level control instructions, which are then issued after feasibility verification. The feedback rolling update module is used to provide rolling updates of unexecuted dynamic boundaries, thermal deficits, and recovery plans based on timestamped execution power, device status, and thermal status feedback.